论文标题
用于扩散桥的分段确定性蒙特卡洛法
A piecewise deterministic Monte Carlo method for diffusion bridges
论文作者
论文摘要
我们将Zig-Zag采样器的使用引入采样条件扩散过程（扩散桥）的问题。 Zig-Zag采样器是一种基于非可逆连续分段确定性马尔可夫过程的无排斥采样方案。类似于布朗运动的莱维·西耶尔斯基（Lévy-Ciesielski）结构，我们以截短的faber-schauder的基础扩展了扩散路径。使用Zig-Zag采样器对基础内的系数进行采样。一个关键的创新是将完全局部算法用于Zig-Zag采样器，该算法允许利用系数的依赖图和亚采样技术所隐含的稀疏结构来降低算法的复杂性。我们在许多示例中说明了所提出的方法的性能。
We introduce the use of the Zig-Zag sampler to the problem of sampling conditional diffusion processes (diffusion bridges). The Zig-Zag sampler is a rejection-free sampling scheme based on a non-reversible continuous piecewise deterministic Markov process. Similar to the Lévy-Ciesielski construction of a Brownian motion, we expand the diffusion path in a truncated Faber-Schauder basis. The coefficients within the basis are sampled using a Zig-Zag sampler. A key innovation is the use of the fully local Algorithm for the Zig-Zag sampler that allows to exploit the sparsity structure implied by the dependency graph of the coefficients and by the subsampling technique to reduce the complexity of the algorithm. We illustrate the performance of the proposed methods in a number of examples.
